Relations between the sides of a triangle, and everythign is underroot

In summary, the conversation discusses the difficulty in proving a given relation involving square roots and their cyclic order. It is suggested to potentially use the cosine rule or consider a geometric constraint in order to manipulate the expression and prove the relation.
  • #1
dharavsolanki
79
0
The relation to be proved looks pretty simple. However, there is no evident point from whih I can start.

How do I start relating quantities that are under root? The cyclic order of the sides on the left side is reminiscent of the cosine rule, but that's just it!

Plus the right hand side has the sum of three surds. I don't see a drect arrival at such an expression. So, where do we start from?

Is there a relation to be picked up which can then be manipulated to reach both the sides? Or some geomterical constraint that we need to be thinking about?
 

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  • #2
To prove:

root a + b -c + root b + c -a + root c +a - b is less than equal to root a + root b + root c
 

1. What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

2. How do you find the length of a side in a right triangle using the Pythagorean theorem?

To find the length of a side in a right triangle, you can use the formula a² + b² = c², where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse. Rearranging the equation to solve for c, you can take the square root of both sides to find the length of the hypotenuse.

3. What is the relationship between the sides of a 45-45-90 triangle?

In a 45-45-90 triangle, the two shorter sides (the legs) are equal in length and the length of the hypotenuse is equal to the length of one leg times the square root of 2.

4. How do you determine if a triangle is a right triangle using the Pythagorean theorem?

To determine if a triangle is a right triangle, you can use the Pythagorean theorem. If the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

5. Can the Pythagorean theorem be used for non-right triangles?

No, the Pythagorean theorem can only be used for right triangles. For other types of triangles, you would need to use other formulas such as the Law of Cosines or the Law of Sines to find the length of the sides.

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